Show that the substitution y transform the differential equation =(yx) into a separable differential equation b)...

  

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Show that the substitution y transform the differential equation =(yx") into a separable differential equation b) Use the method above to solve (x-1), y(1)=-1. (20) 2. Given that esin2x is a solution of Find the general solution. (20) 3. Solve the differential equation 2xy +5xy+y=ax + bx where a and b are real constants +30y=0. ds 4 (20) 4. Find the power series solution in powers of (x-1) of the initial-value problem +2y= 0, y(1)=2, y(1)=4. Show that the substitution y transform the differential equation =(yx") into a separable differential equation b) Use the method above to solve (x-1), y(1)=-1. (20) 2. Given that esin2x is a solution of Find the general solution. (20) 3. Solve the differential equation 2xy +5xy+y=ax + bx where a and b are real constants +30y=0. ds 4 (20) 4. Find the power series solution in powers of (x-1) of the initial-value problem +2y= 0, y(1)=2, y(1)=4.